Seminar

In 1994, the field of quantum computing had a significant breakthrough when Peter Shor introduced a quantum algorithm that factors integers in (probabilistic) polynomial time.  In these talks, I'll explain the mathematical aspects of Shor's algorithm.
Part II will follow on 3/5.

One approach to ion-photon entanglement relies on transitions from 2P3/2 to the low-lying 2D3/2 and 2D5/2 states at 1345 nm and 1650 nm in Yb+ [1]. Here Purcell enhancement is crucial for achieving good performance in the context of quantum networking. In support of this effort, we developed a monolithic, fiber-coupled Fabry–Pérot cavity integrated with a blade trap that operates at cryogenic temperatures. One of the cavity mirrors is bonded to a metalens that mode-matches cavity light to a single-mode fiber.

Instabilities, where initially small fluctuations seed the formation of large-scale structures, govern the dynamics in various fluid flows. The Rayleigh-Taylor instability (RTI) is an iconic example that leads to the development of mushroom-shaped incursions when immiscible fluids are accelerated into each other. RTI drives structure formation throughout science and engineering including table-top oil and water mixtures; supernova explosions; and inertial confinement fusion.  Despite its ubiquity, controlled laboratory RTI experiments are technically challenging.

A cryptographic proof of quantumness is a hypothetical test that could be used to prove a quantum computational advantage based on hardness assumptions from cryptography.  An experimental realization of such a test would be a major milestone in the development of quantum computation.  However, error tolerance is a persistent challenge for implementing such tests: we need a test that not only can be passed by an efficient quantum prover, but one that can be passed by a prover that exhibits a certain amount of computational error.

We extend entropy production to a deeply quantum regime involving noncommuting conserved quantities. Consider a unitary transporting conserved quantities (“charges”) between two systems initialized in thermal states. Three common formulae model the entropy produced. They respectively cast entropy as an extensive thermodynamic variable, as an information-theoretic uncertainty measure, and as a quantifier of irreversibility. Often, the charges are assumed to commute with each other (e.g., energy and particle number). Yet quantum charges can fail to commute.

In this talk, I will present a construction of symmetric informationally complete POVMs (SIC-POVMs), a special class of quantum measurements whose existence in all dimensions was conjectured by Zauner in 1999. Equivalently, these are maximal sets of d^2 equiangular lines in ℂ^d. Our approach introduces an explicit mathematical object, the ghost SIC, built from number-theoretic properties of a special modular function, and we show that it is Galois conjugateto an actual SIC.

This talk will review our recent work on classical and quantum glasses. I will start with a discussion of spin glasses from the perspective of chaos theory.

Unlike the traditional study of algorithms which attempts to solve a certain task using minimal space and time resources, I will discuss data structures to solve certain algorithmic tasks after an initial pre-processing phase. The interest here is to study the tradeoffs between the resources such as the space and time required to perform the algorithmic task when asked a query; and the resources in the pre-processing phase such as the time required to prepare the data structure or its size.

I'll give theorems characterizing finite-dimensional quantum theory's framework of 

In this talk, I present an experimental realization of a quantum absorption refrigerator formed from superconducting circuits. The refrigerator is used to reset a transmon qubit to a temperature lower than that achievable with any one available bath. The process is driven by a thermal gradient and is autonomous -- requires no external control. The refrigerator exploits an engineered three-body interaction between the target qubit and two auxiliary qudits coupled to thermal environments, formed from microwave waveguides populated with thermal photons.